The Cauchy problem for the fourth-order Schrödinger equation in H s
- 1 July 2021
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 62 (7), 071501
- https://doi.org/10.1063/5.0045390
Abstract
We consider the fourth-order Schrödinger equation i∂tu + Δ2u + μΔu + λ|u|αu = 0 in , with , μ = ±1 or 0, 0 < s < 4, 0 < α, and (N − 2s)α < 8. We establish the local well-posedness result in by applying Banach’s fixed-point argument in spaces of fractional time and space derivatives. As a by-product, we extend the existing H2 local well-posedness results to the whole range of energy subcritical powers and arbitrary .
Funding Information
- National Natural Science Foundation of China (11771389, 11931010, 11621101)
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